In wideband wireless communications, frequency-selective, or multipath, fading is a particular problem as it degrades channel quality. Multicarrier modulation is an effective technique to combat multipath fading. In this modulation scheme, the transmission bandwidth is divided into a plurality of carriers (called subcarriers) to utilize the frequency diversity in a frequency-selective fading environment and thereby enable high-quality wireless transmission. Orthogonal Frequency Division Multiplexing (OFDM) is also included in this technique.
A main disadvantage of the multicarrier technique is that multicarrier signals inherently exhibit a high peak power (or peak-to-average power ratio). Linear amplifiers having a wide dynamic range are needed to maintain system linearity. However, linear amplifiers are not only expensive, but their power efficiency is also very low. On the other hand, using inexpensive nonlinear amplifiers involves the problem of nonlinear distortion, resulting in degradation of performances, since these amplifier are operated in their saturation regions. These problems have been regarded as a bottleneck impeding the commercial implementation of this technique.
There are two main approaches to solving these problems: (1) by restricting the signal input and (2) by restricting the signal output. The former approach, mainly employing coding technique, is performed so as not to produce signal patterns that increase peak power, and no degradation in performances occurs. Furthermore, if the minimum distance of the code can be increased, it is also possible to improve the bit-error rate—BER performance. The latter approach, such as clipping technique which clips the signal before amplification, is also an effective technique for the peak reduction. This is because the large peaks occur with very low probability. This technique however causes both the BER performance degradation and the spectral efficiency reduction. There is also a technique that normalizes the entire signal envelope level to the threshold value, but this also causes the performance degradation due to the loss of the S/N ratio. The former technique is therefore preferred for providing wideband high-quality wireless transmission.
Complementary sequence (complementary code) has the proper of both peak reduction and error correction, and is being studied for application to the multicarrier modulation scheme. This code can be applied to M-ary phase shift keying (MPSK) modulation. This code achieves the coding rate R=(log2N+1)/N, the minimum distance dmin=√{square root over (N/2)} d, and the peak power Ppep=2/N P(N) in the case of N carriers, where d is the minimum distance between signal points, and P(N) (=N2) is the peak power of N carriers without coding. For example, in the case of four carriers, R=¾, dmin2=2d2, and Ppep=P(4)/2, while in the case of eight carriers, R=½, dmin2=4d2, and Ppep=P(8)/2. Accordingly, since the coding rate of complementary code decreases as the number of carriers increases, degradation in transmission efficiency is unavoidable even if the improvement of the error-correction capability is considered. It is of course possible to operate the system as a four-carrier system by dividing the eight carries into two four carriers, but if this technique is used, the coding rate of R>¾ is not available.
On the other hand, N carriers are represented by MN signal patterns (M is the number of modulated signal points). It is well known to reduce peak power by measuring the peak envelope power (PEP) levels of all signal patterns, ranking them in the order of envelope levels and encoding using only the patterns in the lower half of the ranking. This means that the peak power can be reduced by adding only one redundant bit. Moreover, the reduction effect, ΔPPEP (10 log (P(N)/Ppep)[dB]), achieved by this one-bit redundancy increases as N is increased. Therefore, increasing N should, in effect, lead to an increase in coding rate. However, in the above-described complementary code, the coding rate decreases with increasing N; therefore, it cannot fully meet this phenomenon. It should also be noted that, with the technique that uses the patterns in the lower half of the PEP ranking, the error-correction capability cannot be obtained. Furthermore, since there is no logical between the signal input and the code assigned to it, logic circuits cannot be used, which leaves no other choice but to use a mapping memory such as a ROM. Using a mapping memory becomes unrealistic when the number of carriers increases.